I was told by the chef at Ruth's Chris that the best place to buy meat is Costco. I've gotten a lot of good meat there, and also from Whole Foods but they're quite expensive. I typically wouldn't buy meat from the Asian markets.
No Costco membership. Maybe someday when we have a garage to store our extra junk. Somebody recommended Whole Foods to me the other day for corned beef (and he keeps pretty kosher), so I guess the meat department there is quite reputable. I'll give it a try next time we make wontons. We've also heard good things about Iowa Meat Farms.